A rectangular yard with an area of 50m squared is to be fenced on three sides. Minimizing the perimeter will minimize the cost of the fence. Conduct an investigation to determine the shape 0f the yard with the minium perimeter.

Question

I sqaure rooted the 50m and I got 7.07 which then I added 3 times to get the perimeter since has only three sides which then i got 21.21 and i went completely wrong from after that when i double check the answer.... appearetly the real answer is 5m by 10m and I don't how they got it when i was taught to square root the area when you dont know the perimeter...

Answer 1

determine the shape? to minimize perimeter? And you say 5x10?
The minimum perimeter for any geometric shape is circle, in this case with a side already fenced, the shape will be a semicircle.

radius of semicircle:
50=1/2 PI r^2
r= sqrt (10/pi)
minimum perimeter= PI(radius)
= pi sqrt (10/pi)=sqrt10pi

Answer 2

if it is a circle why does it say RECTANGUlAR yard with a area of 50m sqaured

Answer 3

It started out as a rectangular shape. I have no idea why the problem was worded this way. To me, if they wanted it to remain a rectangular shape, they would have asked for the new dimensions of the rectangle of area 50 with three sides fenced.
So I have no idea why it is worded, but the shape to minimize such an area will be a shape of a semicircle.
Could be the teacher didn't mean "determine the shape"

Answer 4

square rooting implies that the yard is square ... from the result of your answer, this is not the case

the "perimeter" in this problem, is only three sides

A = L * W = 50

P = L + 2W

a good investigation might consist of a table comparing L, W, and P
... remember, you're looking for a minimum P